Abstract
Methods of utilizing independent component analysis (ICA) give little guidance about practical considerations for separating single-channel real-world data, in which most of them are nonlinear, nonstationary, and even chaotic in many fields. To solve this problem, a three-step method is provided in this paper. In the first step, the measured signal which is assumed to be piecewise higher order stationary time series is introduced and divided into a series of higher order stationary segments by applying a modified segmentation algorithm. Then the state space is reconstructed and the single-channel signal is transformed into a pseudo multiple input multiple output (MIMO) mode using a method of nonlinear analysis based on the high order statistics (HOS). In the last step, ICA is performed on the pseudo MIMO data to decompose the single channel recording into its underlying independent components (ICs) and the interested ICs are then extracted. Finally, the effectiveness and excellence of the higher order single-channel ICA (SCICA) method are validated with measured data throughout experiments. Also, the proposed method in this paper is proved to be more robust under different SNR and/or embedding dimension via explicit formulae and simulations.
Highlights
As one of the most attractive solutions for the blind source separation (BSS) problem, independent component analysis (ICA) has a strong practical background and wide applications in multiway data analysis such as biomedicine [1], image processing [2], telecommunications [3], geophysical research field [4, 5], and physics of musical instruments [6, 7], because it is a combination of informationism, optimal theory, probability, matrix theory, and mathematical statistics
In intuitive way a segmentation combined with a ICA approach was already proposed to get information on the very long-period waves from water-level oscillations [11, 12], in which the ICA, the intertime occurrence, and the reconstruction of asymptotic dynamics are adopted after a preanalysis in the frequency domain
ICA appears more appropriate in the investigation of nonlinear systems than the analyses based on the Fourier transform, even though several tidal behaviours have been pointed out by frequency-domain methods
Summary
As one of the most attractive solutions for the blind source separation (BSS) problem, independent component analysis (ICA) has a strong practical background and wide applications in multiway data analysis such as biomedicine [1], image processing [2], telecommunications [3], geophysical research field [4, 5], and physics of musical instruments [6, 7], because it is a combination of informationism, optimal theory, probability, matrix theory, and mathematical statistics. In a dynamical embedding framework, the measured data can be assumed to be generated by the nonlinear interaction of just a few degrees of freedom, with additive noise, and suggests the existence of an unobservable deterministic generator of the observed data In this case the reconstructed phase space (RPS) can be used to uncover as much information as possible about the underlying generators based only on the measured data [22], and the ICA algorithm could be performed on the embedding matrix to exact its underlying ICs in the SCICA method proposed by James and Lowe [23, 24]. R denotes real number domain. σ and σdenote the true value and the estimate of variable σ, respectively
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